Spectral lattices of Rmax,+-formal contexts

  • Authors:
  • Francisco J. Valverde-Albacete;Carmen Peláez-Moreno

  • Affiliations:
  • Dpto. de Teoría de la Señal y de las Comunicaciones, Universidad Carlos III de Madrid, Leganés, Spain;Dpto. de Teoría de la Señal y de las Comunicaciones, Universidad Carlos III de Madrid, Leganés, Spain

  • Venue:
  • ICFCA'08 Proceedings of the 6th international conference on Formal concept analysis
  • Year:
  • 2008

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Abstract

In [13] a generalisation of Formal Concept Analysis was introduced with data mining applications in mind, K-Formal Concept Analysis, where incidences take values in certain kinds of semirings, instead of the standard Boolean carrier set. Subsequently, the structural lattice of such generalised contexts was introduced in [15], to provide a limited equivalent to the main theorem of K-Formal Concept Analysis, resting on a crucial parameter, the degree of existence of the objectattribute pairs φ. In this paper we introduce the spectral lattice of a concrete instance of K-Formal Concept Analysis, as a further means to clarify the structural and the K-Concept Lattices and the choice of φ. Specifically, we develop techniques to obtain the join- and meet-irreducibles of a Rmax,+-Concept Lattice independently of φ and try to clarify its relation to the corresponding structural lattice.